Question: Find $t$ such that $(t,5)$ lies on the line through $(0,3)$ and $(-8,0)$.
Solution: The slope of the line through $(0,3)$ and $(-8,0)$ is $(0-3)/(-8-0) = 3/8$. If $(t,5)$ is also on this line, then the slope of  the line through $(t,5)$ and $(0,3)$ must also be $3/8$.  Therefore, we must have \[\frac{3-5}{0-t} = \frac{3}{8} \implies \frac{2}{t} = \frac{3}{8} \implies (2)(8) = 3(t) \implies t = \boxed{\frac{16}{3}}.\]